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Search: id:A031971
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| 1, 5, 36, 354, 4425, 67171, 1200304, 24684612, 574304985, 14914341925, 427675990236, 13421957361110, 457593884876401, 16841089312342855, 665478473553144000, 28101527071305611528, 1262899292504270591313
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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p^(3k-1) divides a(p^k) for prime p>2 and k=1,2,3,4.. or p^2 divides a(p) for prime p>2. p^5 divides a(p^2) for prime p>2. p^8 divides a(p^3) for prime p>2. p^11 divides a(p^4) for prime p>2. .. p^2 divides a(2p) for prime p>3. p^3 divides a(3p) for prime p>2. p^2 divides a(4p) for prime p>5. p^3 divides a(5p) for prime p>3. p^2 divides a(6p) for prime p>7. .. p divides a(2p-1) for all prime p. p^3 divides a(2p^2-1) for all prime p. p^5 divides a(2p^3-1) for all prime p. .. p divides a((p-1)/2) for p=5,13,17,29,37,41,53,61..=A002144 Pythagorean primes: primes of form 4n+1. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 21 2006
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FORMULA
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a(n) is asymptotic to (e/(e-1))*n^n - Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 17 2003
a(n) = Zeta[ -n] - Zeta[ -n,n+1]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 21 2006
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MAPLE
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f := n->sum('i'^n, 'i'=1..n);
a:=n->sum(mul(k-1, j=2..n), k=2..n): seq(a(n), n=2..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2007
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MATHEMATICA
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Zeta[ -n] - Zeta[ -n, n+1] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 21 2006
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CROSSREFS
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A diagonal of array A103438.
Cf. A002144.
Sequence in context: A008785 A081918 A062024 this_sequence A132686 A118018 A156355
Adjacent sequences: A031968 A031969 A031970 this_sequence A031972 A031973 A031974
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Chris du Feu (chris(AT)beckingham0.demon.co.uk)
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